Order flow imbalance effects on the German stock market...ORIGINAL RESEARCH Order ﬂow imbalance...

ORIGINAL RESEARCH

Order flow imbalance effects on the German stockmarket

Michael Hanke1 • Michael Weigerding1

Received: 17 July 2014 / Accepted: 9 October 2015 / Published online: 24 October 2015

� The Author(s) 2015. This article is published with open access at Springerlink.com

Abstract Order flow imbalance refers to the difference between market buy and

sell orders during a given period. This paper is the first study to examine effects of

order flow imbalance on returns of stocks traded on the German Xetra trading

system on a daily basis. In contrast to previous studies on other markets, we control

for unobserved effects using a fixed-effects panel regression. For the concurrent (or

conditional) relation between order imbalance and returns, our results confirm those

of the literature. For the question of return predictability from past order imbalances

(unconditional relation), our results are partly confirmatory. In addition, we provide

evidence for size and liquidity effects and analyze changes in imbalance effects

during the financial crisis.

Keywords Order imbalance � Return predictability � Panel regression

1 Introduction

Neoclassical financial theory argues that the arrival of news is the major driver of

asset prices. Focusing particularly on those aspects that neoclassical finance usually

assumes away, the (more recent) literature on market microstructure provides a

wealth of models featuring effects on market prices that could not be explained in

the neoclassical framework. In this literature, a number of papers investigate the

effect of buying/selling pressure currently prevailing in the market for an asset on its

price movements. A popular measure of buying/selling pressure in intermediated

markets, where market makers ensure liquidity, is order (flow) imbalance, which

& Michael Hanke

[email protected]

1 Institute for Financial Services, University of Liechtenstein, Furst-Franz-Josef-Strasse, 9490

Vaduz, Liechtenstein

123

Business Research (2015) 8:213–238

DOI 10.1007/s40685-015-0025-0

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measures the disparity between buyer- and seller-initiated trades (a precise

definition will be provided in Sect. 3.1.1).

The present paper analyzes effects of order imbalance on daily returns of German

stocks. It contributes to the empirical literature on order imbalance effects in stock

returns in various ways. First, up to now, there are no studies investigating

imbalance–return relations for German stocks. An advantage of the German data

over most US data is that all trades are identified as either buyer- or seller-initiated,

thus avoiding errors from the use of trade classification algorithms. Second, while

most of the literature uses time series regressions, we rely on fixed-effects panel

regression as described in Sect. 3.2. Third, studies based on a recent sample of daily

order imbalances do not seem to exist: stock markets worldwide become more

efficient, and it seems interesting whether effects documented for the 1990s still

persist at daily frequencies. Therefore, in the present paper, we scrutinize concurrent

and unconditional relations for the German market and provide results for recent

day-to-day effects. Fourth, we document size and liquidity effects in the imbalance–

return relation. Fifth, in contrast to the previous literature, we find imbalance effects

to be weaker for very high levels of order imbalance. Sixth, we are the first to

analyze imbalance effects during the financial crisis and show that the concurrent

relation has increased in that period.

The paper is organized as follows: Section 2 provides a review of previous

papers on order imbalance, which positions our results in the context of the existing

literature. Section 3 defines the variables and the regression models used. Section 4

describes our data together with the sample selection criteria we applied. Section 5

discusses our results and compares them to those in the literature. Section 6

concludes.

2 Review of the literature and contribution

In this section, we provide an overview of the literature on order imbalance, its

causes, and its effects on asset returns. We start with theoretical explanations for the

existence of order imbalance and its effects on asset prices. This will be followed by

a comparison of previous empirical results.

2.1 Theoretical models related to order imbalance

A very simple model of an intermediated stock market is presented by Roll (1984).

A risk-neutral market maker sets quotes for trading with a non-discretionary

liquidity trader. The assumption of an efficient market implies that the quotes

remain unchanged unless new information arrives. In this situation, a market buy

order will be executed at the ask and can either be followed by a trade at the same

price or at a lower price (the bid). This induces a negative link between order

imbalance and subsequent price changes. The resulting bid-ask bounce effect

creates negative first-order autocorrelation in returns calculated from traded prices

measured over adjacent time intervals (e.g., daily closing prices).

214 Business Research (2015) 8:213–238

123

When the market maker is assumed to be risk-averse instead of risk-neutral,

trading leads to (potentially undesirable) changes in his risk position. A model in

this spirit is studied by Stoll (1978). Starting from an initially optimal portfolio, this

implies two types of risks: first, any trade changes the overall risk of the market

maker’s portfolio, moving it to a risk level different from the market maker’s target

level. Second, assuming the initial portfolio was perfectly diversified, any trade

moves the portfolio away from perfect diversification by increasing unsystematic

risk. Trying to reduce this inventory holding risk, the market maker will adjust the

level of quotes to induce trading at the desired side of the spread, which—at first—

results in a positive link between order imbalance and price change. Once

successful, quotes are reset to their initial values. The resulting higher probability

for a price change that is negatively related to order imbalance has been termed

induced order arrival effect by (Huang and Stoll 1994, p. 183).

Acknowledging that some traders may have private information not yet

incorporated in market prices, market makers anticipate possible losses due to

informed trading (adverse selection) by widening bid-ask spreads. This allows them

to recover losses to informed traders through increased profits from trading with

liquidity traders (Bagehot 1971, p. 13). The risk of other traders obtaining the same

information creates time pressure on informed traders (Glosten 1994, p. 1151),

which leads to a preference for market orders or aggressively priced limit orders for

exploiting private information (Harris 1998, pp. 1ff.). By pushing the price towards

the asset’s fundamental value, informed trading creates a positive link between

order imbalance and price changes (Huang and Stoll 1997, p. 999).

Private information may also lead to serial correlation in trades, since informed

investors try to prevent conveying their information to the market by splitting their

orders and buy or sell repeatedly until the price has moved to the extent indicated by

their information (Kyle 1985, p. 1330). Similar effects occur when institutions split

large orders to reduce price impact, sometimes over several days (Chan and

Lakonishok 1995, p. 1152). Herding (see, e.g., Lakonishok et al. 1992) e.g., due to

peer group pressure (see, e.g., Lee et al. 2004, p. 332) information cascades (Chiao

et al. 2011, p. 132) or processing correlated (Chiao et al. 2011, p. 132) or even the

same public (Lakonishok et al. 1992, p. 26) or private information (Hasbrouck and

Seppi 2001, p. 386), positive feedback trading (Lakonishok et al. 1992, p. 26) or

exogenous factors (Hasbrouck and Seppi 2001, p. 386) will also lead to serial

correlation in trades. This amplifies the inventory holding and adverse selection

effects described above.

Several more recent models study the interrelation of all these effects together

with their total impact on market prices. Examples for such models include Huang

and Stoll (1994, 1997); Stoll (2000); Llorente et al. (2002); Chordia and

Subrahmanyam (2004), and Subrahmanyam (2008). Some of the effects amplify

each other, while others act in opposite directions. Table 1 lists the component

effects together with their respective signs.

Which of the effects dominates depends on the circumstances. However, when

excluding bid-ask bounces using mid-quote returns, most of the remaining effects

point towards a positive predictive relation between order imbalance and subsequent

price changes. Chordia and Subrahmanyam (2004, p. 487) argue that adding current

Business Research (2015) 8:213–238 215

123

order imbalance as an explanatory variable will change the sign of the coefficients

of past order imbalances to negative. This is due to the autocorrelation in trades.

2.2 Empirical results on order imbalance effects in asset returns

The majority of empirical studies confirms the signs of imbalance–return relations

suggested by market microstructure theory: contemporaneous order imbalance is

positively linked to returns whereas conditional lags are negatively linked. The

unconditional first lag is positive, whereas higher lags are either negative or

insignificant. However, the strength of these dependencies differs across markets

and sample periods analyzed.

Existing empirical studies can be broadly classified by data frequency. We will

first discuss results for intra-day data before covering studies based on daily or

lower observation frequencies. Table 2 summarizes information on intra-day

studies, the samples used, and their findings. Most intra-day studies document a

strong contemporaneous relationship with decreasing conditional lags. Shifting the

relation by one interval, stock market studies document a strong unconditional first

lag for observation intervals of up to several minutes. Order imbalances have more

explanatory power for less efficient markets. Higher unconditional lags are mostly

insignificant.

Harford and Kaul (2005) document a strong concurrent relation on the US stock

market for 1986 and 1996. In the 2000s, this is confirmed for special samples such

as top losers or gainers by Su and Huang (2008), Su et al. (2009b), Su et al. (2011),

and Huang et al. (2012). Apart from stocks, Locke and Onayev (2007, S&P 500)

and Huang and Chou (2007, Taiwan) find strong intra-day relations for index

futures. The relation for higher lags is weak or even insignificant when controlling

for concurrent imbalance.

Studies with more recent sample periods mainly focus on the unconditional

lagged relation. For NYSE stocks, Chordia et al. (2008) find significant coefficients

for lag 1 based on 5-min returns. The relation is stronger for smaller firms. Their

sample covers the largest 500 stocks from 1993 to 2002. The more detailed results

for 1996, 1999 and 2002 in Chordia et al. (2005) (covering the biggest 150 NYSE

stocks) reveal that in earlier years, the link was significant up to an interval length of

30 min. In 2002, however, there is no significant link beyond five minutes. In this

regard, the Japanese stock market seems to be as efficient as its US counterpart.

Table 1 Effects of order imbalance on subsequent price changes implied by theoretical models

Component effect Direction

Bid-ask bounce �Inventory holding ?

Induced order arrival �Adverse selection ?

Serial correlation ?


123

Table

2Empirical

studiesdealingwithorder

imbalance

andreturn

(intra-day

data)

Study

Market

Sam

ple

period

Relationofcurrentreturn

andorder

imbalance

lag

Concurrentlag

Conditional

firstlag

Unconditional

firstlag

Unconditional

secondlag

Harford

andKaul(2005)

NYSEstocks

1986and1996

Positive***

Negative***a

Chordia

etal.(2005)

NYSEstocks

1996,1999,and

2002

Positive**b

Chordia

etal.(2008)

NYSEstocks

Jan.1993–Dec.

2002

Positive***

VisaltanachotiandYang

(2010)

NYSEnon-U

S

stocks

Jan.2005–Dec.

2005

Positive***

Huanget

al.(2012)

NYSEtoplosers

Jan.2005–Dec.

2005

Positive(100%,

0%)

Negative(0

%,94%)

Negative(2

%,83%)

Insignificant(8

%,

15%)

SuandHuang(2008)

NASDAQ

top

gainersc

Oct.2004–Nov.

2004

Positive(93%,

0%)

Negative(0

%,22%)

Insignificant(1

%,

6%)

Insignificant(7

%,

4%)

Suet

al.(2009b)

NASDAQ

stocksc,d

Oct.2004–Feb.

2005

Positive(96%,

0%)

Insignificant(7

%,

16%)

Insignificant

(12%,6%)

Insignificant(6

%,

10%)

Suet

al.(2011)

NASDAQ

top

losers

Dec.2005

Positive(82%,

0%)

Negative(2

%,85%)

Negative(2

%,79%)

Insignificant(0

%,

2%)

Suet

al.(2009a)

NASDAQ

top

gainers

Jul.2006–Dec.

2006

Positive(57%,

2%)

Insignificant

(11%,11%)

Insignificant(11%,

5%)

Insignificant(4

%,

11%)

VisaltanachotiandLuo

(2009)

Thai

stockse

Jan.1996–Oct.

2003

Insignificant

Insignificant

Jianget

al.(2011)

Chinesestocksf

Jan.2006–Dec.

2006

Positive***

Yam

amoto

(2012)

NIK

KEI225stocks

Sep.2006–Aug.

2007

Positive***

LockeandOnayev

(2007)

S&P500future

Jan.1998–Dec.

2001

Positive***

Negative***


123

Table

2continued

Study

Market

Sam

ple

period


andorder

imbalance

lag

Concurrentlag

Conditional

firstlag

Unconditional

firstlag

Unconditional

secondlag

HuangandChou(2007)

Taiwan

index

future

Jul.2001–Jun.

2002

Positive***

Positive***

ChangandShie

(2011)

Taiwan

index

future

Oct.2006–Sep.

2007

Insignificantg

Studiesaregrouped

bymarket

andsorted

bysample

period.Thepercentageofsignificantlypositiveandsignificantlynegativecoefficients

isgiven

inparentheses

if

available

(tim

eseries

analysesforsingle

stocks).In

theother

cases,***,**,and*denote

significance

atthe1,5,and10%

levels,respectively.Unless

stated

otherwise,

theresultsreferto

5-m

indata.

Resultsforthenumber

measure

oforder

imbalances(cf.Sect.3.1.1)arereported

whereavailable

aInsignificantduringthelast

tradinghourofaday

btstatistics

computedfrom

thecross-sectional

distribution

cResultsfor90-s

returnsarereported

dSpeculativeNASDAQ

stocksthat

reachanew

52-w

eekhigh

eResultsfor30-m

inreturnsarereported

fResultsfor10-m

inreturnsarereported

gPositiveandsignificantat

the1%

level

forextrem

epositiveandextrem

enegativeorder

imbalances


123

Yamamoto (2012) documents a strong relationship for intervals of up to five

minutes in a sample covering 2006 and 2007. There is a U-shaped size effect with a

stronger relation for both small and large firms.

In other markets the unconditional link is more persistent. Visaltanachoti and

Yang (2010) compare non-US and US firms and show that imbalances have more

explanatory power for non-US firms, where significant effects last for up to 15 min.

The analysis by Jiang et al. (2011) comprises 20 randomly drawn stocks traded on

the Chinese stock exchanges Shanghai and Shenzhen and extends from 2000 to

2008. The average coefficients are highly significant for 10- and 15-min intervals

before becoming insignificant from 30 min onwards. Chang and Shie (2011) deal

with Taiwanese index futures from 2006 to 2007. At the 5-min observation

frequency, order imbalances are found to be related only to extreme (positive or

negative) returns.

Insignificant or negative unconditional links are documented for samples selected

in a non-random manner. For example, stocks with extremely negative returns show

faster return reversals than other stocks do. Accordingly, Su et al. (2011) and Huang

et al. (2012) find strong negative links at lag 1 for NASDAQ and NYSE stocks,

respectively. Conversely, stocks with extremely positive returns do not show any

significant imbalance–return relation. This is shown for the NASDAQ by Su and

Huang (2008) and Su et al. (2009a, b). The first paper deals with 5-min returns, the

two others with 90-s intervals. In all three time series studies, the percentage of

significantly positive or negative coefficients is low and almost equal. Visaltana-

choti and Luo (2009) find no significant imbalance–return relation for Taiwanese

stocks at a 30-min observation frequency.

Table 3 presents the evidence of studies using daily or lower frequencies. The

strong concurrent imbalance–return relation found for 5–15 min is also present at

daily and weekly intervals. However, it declines markedly when unconditional lags

are examined.

Studies based on daily returns for US stocks focus on the period from 1988 to

1998. They find a strong positive contemporaneous link and a weaker negative link

for conditional lags (see, e.g., Chan and Fong 2000; Aktas et al. 2008; Stoll 2000;

Chordia et al. 2002; Chordia and Subrahmanyam 2004). For the early 2000s, the

positive concurrent relation is confirmed by Bailey et al. (2006) and Shenoy and

Zhang (2007) on Asian markets. Conditional lags, however, are found to be

insignificant. Similar results apply for the FTSE 100 index future from 1993 to 2005

(Ning and Tse 2009, pp. 342–343) and for currency pairs during 2007 (Chen et al.

2012, pp. 606–607). Kao (2011) does not find any relation for the Taiwanese index

futures market over a period from 2008 to 2009.

The evidence for unconditional imbalance–return relations is scarce. Analyzing

NYSE stocks from 1988 to 1998, Chordia and Subrahmanyam (2004) find a strong

positive first-lag relation, which is most pronounced in the three smallest size

quartiles. Chordia et al. (2002) use a similar sample and find a strong negative first-

lag relation for extremely negative returns. However, they do not control for bid-

ask-bounce, which might have biased the results. Studies for Taiwanese stocks (Lee

et al. 2004, pp. 334–335) or currency pairs (Chen et al. 2012, pp. 606–607) do not


123

Table

3Empirical

studiesdealingwithorder

imbalance

andreturn

(daily

andlower

frequencies)

Study

Market

Frequency

Sam

ple

period


andorder

imbalance

lag

Concurrent

lag

Conditional

firstlag

Unconditional

firstlag

Unconditional

secondlag

Chan

andFong(2000)

NYSEstocks

Daily

Jul.1993–Dec.1993

Positive***

Aktaset

al.(2008)

NYSEandAMEX

stocks

Daily

Jan.1995–Dec.1999

Positive***

Stoll(2000)

NYSEstocks

Daily

Dec.1997–Feb.1998

Positive

(63%,0%)

Insignificant

(3%,4%)

Chordia

etal.(2002)

NYSEstocksaggregated

Daily

Jan.1988–Dec.1998

Positive***

Negative***

Insignificanta

Chordia

andSubrahmanyam

(2004)

NYSEstocks

Daily

Jan.1988–Dec.1998

Positive

(100%,0%)

Negative

(3%,31%)

Positive(26%,1%)

Insignificant

(5%,6%)

Kanielet

al.(2008)

NYSEstocks

Weekly

Jan.2000–Dec.2003

Positive***

Subrahmanyam

(2008)

NYSEstocks

Monthly

Jan.1988–Dec.2002

Insignificant

Negative*

Subrahmanyam

(2008)

NYSEstocks

Bim

onthly

Jan.1988–Dec.2002

Negative***

Chan

andFong(2000)

NASDAQ

stocks

Daily

Jul.1993–Dec.1993

Positive***

Stoll(2000)

NASDAQ

stocks

Daily

Dec.1997–Feb.1998

Positive

(71%,0%)

Insignificant

(5%,3%)

Lee

etal.(2004)

Taiwanesestocksb

Daily

Sep.1996–Apr.1999

Insignificant

Baileyet

al.(2006)

Shanghai

index

stocksc

Daily

Oct.2003–Mar.2004

Positive(49%,2%)

Insignificant

(no%

given)

ShenoyandZhang(2007)

Chinesestocks

Daily

Jul.2004–Dec.2004

Positive(82%,0%)

Insignificant

(1%,7%)

Andradeet

al.(2008)

Taiwanesestocks

Weekly

Jan.1994–Aug.2002

Positive***

Negative***

NingandTse

(2009)

FTSE100index

future

Daily

Jan.1993–Dec.2005

Positive***

Insignificant

Insignificant

Kao

(2011)

Taiwan

index

future

Daily

Jan.2008–Dec.2009

Insignificant

Insignificant


123

Table

3continued

Study

Market

Frequency

Sam

ple

period


andorder

imbalance

lag

Concurrent

lag

Conditional

firstlag

Unconditional

firstlag

Unconditional

secondlag

Chen

etal.(2012)

Currency

pairs

Daily

Jan.2007–Dec.2007

Mainly

positive***

Mainly

insignificant

Studiesaregrouped

bymarketandsorted

byfrequency

andsampleperiod.Thepercentageofsignificantlypositiveandsignificantlynegativecoefficientsisgiven

inparentheses

ifavailable(tim

e

series

analysesforsinglestocks).Otherwise,***,**,and*denotesignificance

at1,5,and10%,respectively.Resultsforthenumber

measure

oforder

imbalances(cf.Section3.1.1)arereported

whereavailable

aNegativeandsignificantat

the1%

level

forextrem

enegativeorder

imbalances

b30largestTaiwanesestocksaggregated

cResultsforinstitutional

investors

arereported


123

find any pronounced relationships. Kao (2011) finds a strong positive unconditional

first lag only for extreme positive imbalances.

A positive relation between order imbalances and returns has been documented

even beyond the daily horizon. Studying Taiwanese stocks from 1994 to 2002,

Andrade et al. (2008) find a significantly positive contemporaneous relation for

weekly data. Conditional lags are significantly negatively related. In the cross-

sectional regression of Kaniel et al. (2008), the unconditional first lag is significantly

positive. The study analyzes order imbalances of individual investors trading NYSE

stocks from 2000 to 2003. Subrahmanyam (2008) aggregates order imbalances to

monthly data. His sample consists of NYSE stocks from 1988 to 2002. The first and

the second unconditional lags are negatively related to returns. The relation is

significant for the second lag and can be traced back to mid-sized firms.

Whereas the initial imbalance effects on US markets are strong and last only for

several minutes, offloading inventories seems to occur gradually and over longer

time periods of sometimes up to several weeks. This is suggested by the fact that a

positive link can be found even at daily and weekly frequencies and for both

concurrent and unconditional first lags. For Chinese stock and future markets the

daily relation is only significant for the concurrent view. Various size effects have

been documented, but vary in nature from market to market.

3 Methodology

3.1 Variables

3.1.1 Order imbalance

In the literature, three major approaches to measuring order imbalance are used: one

is based on the number of buy and sell orders, another considers also the size of

orders (i.e., the number of shares in each order), and yet another accounts also for

the current share price by multiplying it with the order size. Most of the literature on

order imbalance uses the first approach, sometimes combined with the second. A

number of studies favor the use of the simple number measure: Jones et al. (1994)

find a much stronger effect of the number of trades (as compared to trading volume)

on return volatility. On a sample of NYSE stocks observed over roughly 10 years,

Chordia and Subrahmanyam (2004) find a markedly higher correlation between

returns and order imbalance when the latter is measured using the number measure

approach. Scaling order imbalance by the total number of trades may diminish

autocorrelation (Chordia and Subrahmanyam 2004, p. 498) but has the advantage of

allowing for meaningful comparisons across stocks despite differences in liquidity.

Hence, we define the order (flow) imbalance for stock i on day t as

Ii;t ¼No. of buyer-initiated tradesi;t � No. of seller-initiated tradesi;t

Total no. of tradesi;t: ð1Þ

Xetra allows for identification of every single transaction as either buyer- or seller-

initiated, even for transactions within the bid-ask spread. This avoids any need for


123

applying the Lee and Ready (1991) trade classification algorithm used in many

previous quote-driven studies, see e.g., Chan and Fong (2000, p. 254), Chordia and

Subrahmanyam (2004, p. 494), Yamamoto (2012, p. 9). Moreover, by including

both market orders and marketable limit orders (marketable limit orders are limit

buy orders above the ask quote or limit sell orders below the bid), all traders

demanding immediacy in execution are included. Li et al. (2010) argue that with-

drawing a limit buy (sell) order has the same effect as submitting a limit sell (buy)

order. Including such canceled orders leads to a higher explanatory power of order

imbalance for concurrent returns. Unfortunately, our dataset does not contain

information on canceled limit orders, which precludes us from using this extended

measure of order imbalance.

3.1.2 Returns

We compute daily log returns from the last mid-quotes before the closing auction:

Ri;t ¼ logaski;t þ bidi;t

aski;t�1 þ bidi;t�1

� �; ð2Þ

where aski;t. . . is the last ask quote for stock i before the closing auction of day t andbidi;t. . . is the corresponding bid quote. Using mid-quotes instead of traded prices

avoids any bid-ask bounce effects, which would induce negative first-order auto-

correlation in returns (see, e.g., Roll 1984; Kaul and Nimalendran 1990; Jegadeesh

1990).

When investigating lead–lag relations as in the present study, infrequent trading

may distort the results (see, e.g., Lo and MacKinlay 1990, p. 178). Following the

literature, we deal with this potential problem by focusing on the most liquid stocks

only and eliminating stocks with missing values for order imbalance. The exact

exclusion procedure will be described in Sect. 4.2.

3.2 Regression models and hypotheses

3.2.1 General relation

Our literature review in Sect. 2 shows that there is a large number of papers

investigating the relation between order imbalances and returns. The models used in

these papers can be broadly classified into two categories: one group tries to forecast

returns from (only) past order imbalances (unconditional lagged relation), the other

aims at explaining returns using current and past order imbalances (concurrent and

conditional lagged relation).

In this paper, we investigate both types of relations between order imbalances

and returns. In contrast to most previous studies based on time series regressions,

however, we stack all observations across the stocks in our sample and perform

panel regressions. We account for time- and stock-specific effects by applying the

within transformation (see Wooldridge 2010, p. 302).


123

Unobserved effects like market sentiment might be present in our data, which

may well be correlated with order imbalance. To assess whether the data correspond

rather to a fixed or a random effects model, we perform Hausman (1978) tests.

Estimators for the fixed and random effects model differ significantly (at the 1 %

level) for both unconditional and conditional models. This indicates that a fixed-

effects regression fits the data better.

For a generic variable Y, unit-specific effects are removed using

€Yi;t :¼ Yi;t � �Yi; ð3Þ

where �Yi is the time-average of the observations on Yi. When applied to return data,

this transformation is equivalent to applying the constant-mean-return correction

(see Brown and Warner 1985, pp. 4–5). Time-specific effects are removed by

subsequently applying the within transformation cross-sectionally, i.e.,

~Yi;t :¼ €Yi;t � N�1XNi¼1

€Yi;t; ð4Þ

where N is the total number of stocks in the sample.

The fixed-effects regression model for the conditional lagged relation is specified

as

~Ri;t ¼XKk¼0

bck~Ii;t�k þ ~�ci;t; ð5Þ

where K is the highest order imbalance lag included, and �ci;t is the error term for

stock i at time t. We test whether bck equals zero by means of two-tailed t tests.

The fixed-effects regression model for the unconditional lagged relation is given

by

~Ri;t ¼XKk¼1

buk~Ii;t�k þ ~�ui;t; ð6Þ

with analogous definitions. The null hypothesis of buk ¼ 0 is again tested using two-

tailed t tests.

Preliminary data analyses reveal that the error terms are subject to both

heteroskedasticity and autocorrelation. Robust standard errors are, therefore,

calculated using the methodology suggested by Arellano (1987, pp. 432–433).

3.2.2 Size and liquidity effects

Previous studies suggest that additional variables, such as size and liquidity,

influence the imbalance–return relation. Adverse selection effects, e.g., are

presumably weaker for large firms and liquid stocks due to better analysts’

coverage (Huang et al. 2012, p. 9584) or a stronger presence of informed traders

(Kyle 1985, pp. 1317–1320). However, the impact of liquidity on inventory holding

effects is still unclear. On the one hand, inventory holding effects could be stronger

for illiquid stocks because liquidity providers face difficulties in offloading


123

undesired inventories (Jiang et al. 2011, p. 475). On the other hand, stronger

herding may lead to amplified inventory holding effects for highly liquid stocks (see

Keim and Madhavan 1995, p. 385 or Bailey et al. 2006, p. 14).

We measure size by yearly market capitalization, Ci;t (provided by Datastream

and updated at the beginning of each year), and liquidity by the bid-ask spread, Si;t.

Size and liquidity effects are interrelated. Stocks of large firms are likely to be more

liquidly traded than smaller stocks. The correlation between market capitalization

and bid-ask spread is �0.27 in our sample. Stratifying the sample by size shows that

correlation is highest for the smallest (�0.24) and the largest quintiles (�0.16). The

magnitude of this correlation is not high enough to raise concerns about

multicollinearity problems, but it may be difficult to clearly separate size from

liquidity effects.

We employ regressions including control and interaction variables for market

capitalization and spread. The latter are products of two factors. The first factor is

the corresponding imbalance lag. The second factor accounts for market capital-

ization and spread. Preliminary data analyses show that imbalance effects seem to

be weakest for mid-cap stocks and stronger for large and small stocks. We capture

the resulting U-shape by including ‘‘abnormal’’ market capitalization, Cai;t, which is

defined as follows:

Cai;t :¼ Ci;t � ðNTÞ�1

XNi¼1

XTt¼1

Ci;t

��; ð7Þ

where T is the total number of observations in the sample.

In a first step, we analyze size effects. The regression model for the conditional

relation is

~Ri;t ¼XKk¼0

bck~Ii;t�k þXKk¼0

clck ~Ci;t�k þXKk¼0

dlck ~Ci;t�k � ~Ii;t�k þXKk¼0

fqck ~Cai;t�k

þXKk¼0

gqck ~Cai;t�k � ~Ii;t�k þ ~�ci;t;

ð8Þ

where we test the null hypotheses of clck ¼ 0, dlck ¼ 0, fqck ¼ 0, and gqck ¼ 0 sepa-

rately by means of two-tailed t tests.

The regression model for the unconditional relation is given by

~Ri;t ¼XKk¼1

buk~Ii;t�k þXKk¼1

cluk ~Ci;t�k þXKk¼1

dluk ~Ci;t�k � ~Ii;t�k þXKk¼1

fquk ~Cai;t�k

þXKk¼1

gquk ~Cai;t�k � ~Ii;t�k þ ~�ui;t;

ð9Þ

with analogous definitions.

In the second step, we analyze liquidity effects. The regression model for the

conditional relation is


123

~Ri;t ¼XKk¼0

bck~Ii;t�k þXKk¼0

clck ~Si;t�k þXKk¼0

dlck ~Si;t�k � ~Ii;t�k þ ~�ci;t; ð10Þ

where we test the null hypotheses of clck ¼ 0 and dlck ¼ 0 separately by means of

two-tailed t tests.

The regression model for the unconditional relation is given by

~Ri;t ¼XKk¼1

buk~Ii;t�k þXKk¼1

cluk ~Si;t�k þXKk¼1

dluk ~Si;t�k � ~Ii;t�k þ ~�ui;t; ð11Þ

with analogous definitions.

Finally, we run two regressions (conditional and unconditional) including size

and liquidity interaction terms simultaneously, i.e., we combine Eqs. (8) and (10) as

well as Eqs. (9) and (11).

4 Data

4.1 Initial dataset

Our dataset includes stocks traded on the German Xetra trading system starting from

Feb. 1, 2002, until Sept. 30, 2009 (1950 trading days). For all stocks, the last

available quotes before the closing auction together with order imbalances are

available on a daily basis. In addition, the market capitalization, which is updated

once a year, is used to categorize companies according to size. Quotes and market

capitalization are retrieved from Thomson Reuters Datastream, and the order

imbalances are computed from data provided by the Karlsruher Kapitalmarktdaten-

bank. Data are adjusted backwards for capital measures such as dividend payouts,

stock splits, reverse splits or repurchases.

The sample selection described in Sect. 4.2 will result in one sample of daily

data. To this end, a number of filtering or exclusion criteria are applied to eight

subperiods: the calendar years from 2003 to 2008 and two somewhat shorter

periods, from Feb. 2002 to year-end and from the beginning of 2009 to the end of

September.

4.2 Sample selection

Three filtering criteria are applied to the initial dataset to arrive at the sample used in

our study. First, for the effects we want to examine, insufficient liquidity may distort

the results. For this reason, we follow previous studies in this field (e.g., Chan and

Fong 2000; Lo and Coggins 2006) and exclude stocks with low liquidity. Second,

ex-dividend dates and similar events are dropped. Third, days with missing data are

excluded. We will now provide more details on each of these steps.

To filter out stocks with insufficient liquidity, the initial dataset is analyzed by

subperiods. This is inspired by the empirical observation that liquidity varies

considerably over time for individual stocks. We consider a stock to be sufficiently


123

liquid (or traded sufficiently actively) if order imbalance can be computed for each

single trading day. For each subperiod described in Sect. 4.1, a stock is excluded if

there is one illiquid day or more. Out of 1225 stocks in the initial dataset, 214 stocks

meet this criterion for at least one of the subperiods. Some of the stocks are included

in all subperiods while others meet the selection criterion only in some subperiods,

but not in others.

In a second step, ex-dividend days and days with capital changes (e.g., stock

splits) are excluded. The corresponding dates are obtained from Thomson Reuters

Datastream.

Third, all relevant variables are screened for missing observations. There are 116

days with missing quote data after steps 1 and 2. These days are also excluded for

the corresponding stocks. Bid and ask quotes show a large number of missing values

on Aug. 24, 2009. Since no information about special market circumstances could

be found for this day (CDAX volatility and volume behave normally), this seems to

be a data integrity issue, which is dealt with by eliminating this day for all stocks.

For Continental AG, all quotes are missing from April 2–12, 2002. This stock is,

therefore, dropped for the 2002 subperiod. Market capitalization shows missing

values throughout entire subperiods for six out of the 214 stocks remaining after

steps 1 and 2 (for other stocks, market capitalization shows missing values for some

days. Since it remains constant throughout a year, such temporarily missing data are

not a problem). This leads to two stocks being dropped completely and two other

stocks being removed from the affected subperiods, but retained in the sample in

other subperiods.

4.3 Validity checks

The sample is then checked for data errors and invalid observations. No negative

quotes are detected. Four ask quotes are found to be lower than the corresponding

bid quotes. These observations are dropped from the sample. The remaining order

imbalances, bid-ask spreads, and returns are tested for validity as described in the

following.

First, order imbalance data are checked. Extreme values are rare. Only three

observations differ from the cross-sectional daily average by more than 1.0. Two of

these observations are accompanied by other large order imbalances in the same

direction. Hence, despite these observations looking extreme at first glance, they

seem to validly document the true development of the market at the time. One

observation is dropped from the sample because the extreme imbalance is not

supported by other market variables during a period of five days around the extreme

observation.

Second, absolute spreads larger than 20 % of the bid quote are examined. Four

quote pairs for one stock and two for a second stock violate this criterion and are

excluded for the stocks in question. In addition, IKB Deutsche Industriebank AG

faced an extraordinary decrease in share price, leading to 17 invalid spreads in

December 2008. To avoid any distortion of the results, IKB is dropped from the

2008 subperiod.


123

Third, returns above 50 % or below �50 % are analyzed in detail. On May 25,

2005, there are 17 returns outside of this interval and many more that are larger than

usual. Quotes differ markedly from the quotes on adjacent days. This leads to

another 13 extreme returns for May 26, 2005. There is no unusual economic news

on either of these days, and neither DAX nor CDAX themselves show abnormal

returns or volumes. To ensure data validity, we excluded May 25, 2005 for all

stocks. Aside from May 25 and 26, 2005, there are 13 other extreme return days.

Three of them concern IKB in the subperiod of 2008, which has already been

excluded due to invalid spreads. The remaining 10 extreme returns are deemed to be

valid (and kept in the sample) because quotes before and after the extreme

observation confirm the return development.

4.4 Final data set

Application of the sample selection criteria described in Sect. 4.2 and the validity

checks in Sect. 4.3 reduces the initial dataset of 624,236 daily observations for 1225

stocks to 207,939 observations for 212 stocks. Table 4 provides the number of

stocks in the various subperiods.

Figure 1 shows the number of daily observations by subperiod. The years with

the highest number of observations are 2006–2008. These three years account for

52 % of the total number of observations. The subperiods 2002 and 2009 are shorter

than 12 months. The remaining variation is due to different numbers of stocks

included in the eight subperiods.

Table 5 provides descriptive statistics for order imbalance and return in the final

sample. The percentage of positive order imbalances of 50.08 % documents that

buying and selling pressure are almost exactly balanced. Nevertheless, the standard

deviation of 21.06 % shows that there is considerable variation in our observations.

1.6 % of all observations are below �0.5, and 1.4 % are above 0.5. Although there

is a small tendency towards positive order imbalances, negative returns are more

prevalent.

Standard deviation of order imbalance is not distributed evenly across firm sizes

and liquidity levels. As shown in Table 6, the standard deviation is largest for size

quintile 1 (smallest firms) and decreases steadily to quintile 5 (largest firms). Results

for liquidity quintiles are similar. This indicates that size and liquidity may play an

important role for the explanation of the imbalance–return relation.

To confirm the significance of this pattern, we regress the absolute value of order

imbalance on market capitalization, Ci;t, and spread, Si;t:

Table 4 Number of stocks included in the final sample by subperiod (out of 1225 stocks in the initial

dataset)

Subperiod 2002 2003 2004 2005 2006 2007 2008 2009

# stocks 63 62 86 105 127 169 153 127

Subperiods 2002 and 2009 do not cover the entire year. In total, 212 stocks are included in the sample


123

j~Ii;tj ¼ c ~Ci;t þ d~Si;t þ ~�i;t: ð12Þ

The null hypotheses c ¼ 0 and d ¼ 0 are tested separately using two-tailed t tests.

The results reported in Table 7 show that the absolute value of order imbalance is

related to the bid-ask spread. This relation is significant at the 1 % level. In contrast

to liquidity, market capitalization does not have a significant impact.

Fig. 1 Daily observations included in the final sample by subperiod

Table 5 Descriptive statistics for the final sample (all values in percent)

Order imbalance Return

Mean 0.37 �0.03

Standard deviation 21.05 2.99

Minimum �95.24 �133.18

Maximum 94.74 84.16

Share of positive values 50.08 48.84

Share of negative values 48.69 50.30

Table 6 Standard deviations for order imbalance stratified by size and liquidity (entire sample: 0.211)

Stratified by

Size Liquidity

Quintile 1 0.2675 0.2831

Quintile 2 0.2394 0.2473

Quintile 3 0.2078 0.2081

Quintile 4 0.1637 0.1597

Quintile 5 0.1433 0.1136

Quintile 1 comprises the smallest firms or least-liquid stocks, respectively


123

5 Results

5.1 Conditional lagged relation

Table 8 reports the regression results for the conditional lagged relation. The second

column provides the results for Eq. (5), i.e., using only current and past order

imbalance as explanatory variables. Preliminary analyses suggested to include four

lags of order imbalance. Consistent with previous findings, the coefficient of

concurrent order imbalance is positive and significant. This can be explained by

serially correlated trades induced by order-splitting or herding (cf. Sect. 2.1).

Moreover, as suggested by theory, coefficients of conditional lagged imbalances are

negative and significant. This is because the effect of current order imbalance is

already partially compensated by liquidity providers in the meantime. The negative

relation is strongest on the second lag and wanes with higher lags.

The remaining columns in Table 8 give the results for the conditional relation

when size and liquidity effects are included (Eqs. (8), (10), and both equations

combined). The number of lags included was determined by starting with four lags,

followed by eliminating insignificant higher lags. There are pronounced size and

liquidity effects for concurrent order imbalance. The size interaction coefficients~Ci;t � ~Ii;t are negative and significant at the 1 % level for the concurrent and lag 1

interaction terms. This means that smaller stocks, in general, are more sensitive to

concurrent imbalances than are larger stocks, and that they show a weaker reversal

effect at lag 1. The positive coefficient for the first two lags of ~Cai;t � ~Ii;t confirms the

U-shape on top of the linear relation just described: very small and very large stocks

show higher sensitivity with respect to concurrent order imbalance, and a smaller

reversal effect on the following day.

Liquidity effects are strong on the concurrent and lag 1 interaction terms,

showing positive and significant coefficients. This shows that illiquid stocks have a

stronger concurrent imbalance–return relation, but a weaker reversal on the

following day. The magnitude of these coefficients is somewhat less stable when

including/not including size interaction coefficients together with liquidity. We

interpret this as an effect of the correlation between size and liquidity and a hint that

the size effect may be stronger/more important than the liquidity effect.

Table 7 Dependence of the magnitude of order imbalance on size and liquidity

Variable Coefficient t statistic p value

~Ci;t 0.00 1.50 0.1326

~Si;t 0.01 3.59 0.0003

Fixed-effects panel regression, Eq. (12). Dependent variable: absolute value of order imbalance. Inde-

pendent variables: market capitalization and percentage bid-ask spread. Stock-specific and time-specific

effects are controlled using the within transformation. t statistics and p values are based on robust

standard errors following Arellano (1987)


123

5.2 Unconditional lagged relation

Table 9 shows the regression results for the unconditional lagged relation. Results

for the regression specified in Eq. (6) are presented in the second column. The first

unconditional lagged coefficient is positive and significant, which is consistent with

previous research. However, it is much smaller than the concurrent coefficient from

Table 8 (2:89 � 10�3 vs. 25:88 � 10�3). Thus, the strong contemporaneous effect of

order imbalances wanes markedly already one day later. In addition, the second lag

of order imbalance is negative as expected, but only significant at the 10 % level.

Higher lags are eliminated because they turned out to be insignificant in preliminary

analyses. The fact that the imbalance effect dies out completely within two days is

in contrast to previous studies based on daily data. This may be due to higher

efficiency in stock markets in the 2000s compared to the sample periods of previous

studies given in Table 3.

Columns 3–5 in Table 9 report regression results for Eqs. (9) and (11) as well as

both equations combined. Size interaction coefficients are highly significant for the

unconditional first lag, but insignificant for higher lags. The first-lagged linear

Table 8 Conditional relation with and without size/liquidity effects

Variable General (Eq. 5) Only size (Eq. 8) Only liquidity (Eq. 10) Both size and liquidity

~Ii;t 2588*** 2233*** 2285*** 2088***

~Ii;t�1 �221*** �411*** �334*** �458***

~Ii;t�2 �307*** �285*** �303*** �285***

~Ii;t�3 �191*** �171*** �187*** �171***

~Ii;t�4 �158*** �137*** �155*** �137***

~Ci;t 30*** 31***

~Ci;t � ~Ii;t �105*** �95***

~Ci;t�1 � ~Ii;t�1 �32*** �29***

~Cai;t

�26*** �26***

~Cai;t � ~Ii;t 104*** 93***

~Cai;t�1 � ~Ii;t�1 46*** 43***

~Si;t 16 18

~Si;t � ~Ii;t 471*** 281***

~Si;t�1 � ~Ii;t�1 179*** 94*

Adj. R2 (in %) 30.57 30.73 30.62 30.74

Fixed-effects panel regression, Eqs. (5) (second column), (8) (third column), (10) (fourth column), and

Equations (8) and (10) combined (last column). Dependent variable: daily closing mid-quote return.

Independent variables: concurrent and four lags of daily order imbalance, control and interaction vari-

ables consisting of the corresponding order imbalance lag and market capitalization (incl. ‘‘abnormal

values’’ as defined in Eq. (7)) or order imbalance and percentage bid-ask spread, respectively. Stock-

specific and time-specific effects are controlled using the within transformation. t statistics and p values

are based on robust standard errors following Arellano (1987). Coefficients have been multiplied by 105


123

relation is negative, which means that order imbalances have a stronger impact on

returns from small stocks. The ‘‘absolute relation’’ is positive and supports a U-

shaped pattern (similar to the findings of Yamamoto 2012, on Japanese data) where

mid-sized stocks have a weaker imbalance–return relation than small and large

stocks. Once including size effects the first lag of the imbalance coefficient ~Ii;t�1

becomes insignificant: the interaction between size and order imbalance shows a

higher explanatory power than order imbalance per se.

The unconditional first-lagged relation exhibits liquidity effects as well. The first

interaction coefficient ~Si;t�1 � ~Ii;t�1 is positive and significant at the 5 % level (at the

1 % level when size effects are not included). This shows that returns of illiquid

stocks are more sensitive to order imbalance than are returns of very liquid stocks.

However, similar to the conditional lagged relation discussed in Sect. 5.1, liquidity

effects are again less stable than size effects. A U-shaped liquidity pattern as

suggested by theory (see, e.g., Keim and Madhavan 1995; Bailey et al. 2006) could

not be detected in the data. We initially included also interaction terms based on the

absolute difference of the spread from its mean, defined similar to Eq. (7). The

coefficients were insignificant, and the corresponding terms were dropped from the

final regressions.

5.3 Different order imbalance levels

Previous research finds higher coefficients when confining the analysis to extreme

order imbalances, see Chordia et al. (2002, pp. 124–126) analyzing aggregated

Table 9 Unconditional relation with and without size/liquidityeffects


~Ii;t�1 289*** 15 161*** –49

~Ii;t�2 –56* –46 –54* –46

~Ci;t�1 26*** 26***

~Ci;t�1 � ~Ii;t�1 –48*** –43***

~Cai;t�1

–22*** –22***

~Cai;t�1 � ~Ii;t�1 64*** 60***

~Si;t�1 0 2

~Si;t�1 � ~Ii;t�1 199*** 124**

Adj. R2 (in %) 27.78 27.81 27.78 27.81

Fixed-effects panel regression, Eqs. (6) (second column), (9) (third column), (11) (fourth column), and

Eqs. (9) and (11) combined (last column). Dependent variable: daily closing mid-quote return. Inde-

pendent variables: two lags of daily order imbalance, control and interaction variables consisting of the

corresponding order imbalance lag and market capitalization (incl. ‘‘abnormal values’’ as defined in

Eq. (7)) or order imbalance and percentage bid-ask spread, respectively. Stock-specific and time-specific

effects are controlled using the within transformation. t statistics and p values are based on robust

standard errors following Arellano (1987). Coefficients have been multiplied by 105


123

NYSE stocks, or Chang and Shie (2011, pp. 74–77) covering the Taiwan index

futures market. To see how the effect on returns depends on the level of order

imbalance, we re-run the regressions in Eqs. (5) and (6) on corresponding sub-

samples stratified by the magnitude of order imbalance. Table 10 provides the

results.

The concurrent effect of order imbalance on returns is strongest for small-order

imbalances (jIi;tj\0:2) and decreases for the two categories of higher order

imbalance (0:2� jIi;tj\0:4 and 0:4� jIi;tj, resp.). For the unconditional relation, thecoefficient for the first order imbalance lag increases for higher order imbalances,

but the difference between high and intermediate order imbalance levels is

negligible. This shows that our results are not driven by extreme observations for

order imbalance. Furthermore, this is in contrast to previous studies, which found

higher coefficients when confining the analysis to extreme order imbalances. A

possible explanation is that very large orders may be filled outside the stock

exchange’s regular trading, which is not captured in our sample.

5.4 Financial crisis

Since this paper is the first one on order imbalance effects using data covering the

recent financial crisis, we take the opportunity and analyze the relation between

order imbalance and return during this period of extreme market stress. To this end,

Table 10 Dependence of the imbalance–return relation on the magnitude of order imbalance

Conditional relation

Variable jIi;tj\0:2 0:2� jIi;tj\0:4 0:4� jIi;tj

~Ii;t 3894*** 3031*** 1967***

~Ii;t�1 �283*** �178*** �143*

~Ii;t�2 �305*** �372*** �167*

~Ii;t�3 �211*** �181*** �39

~Ii;t�4 �175*** �158*** �42

Adj. R2 (in %) 30.21 32.84 38.22

Unconditional relation

Variable jIi;t�1j\0:2 0:2� jIi;t�1j\0:4 0:4� jIi;t�1j

~Ii;t�1 149** 203*** 205***

~Ii;t�2 �102** �51 124

Adj. R2 (in %) 30.45 22.42 20.70

Fixed-effects panel regression, Eqs. (5) (upper part) and (6) (lower part). Dependent variable: daily

closing mid-quote return. Independent variables: concurrent and four lags (conditional) or two lags

(unconditional) of daily order imbalance. Stock-specific and time-specific effects are controlled using the

within transformation. t statistics and p values are based on robust standard errors following Arellano

(1987). Coefficients have been multiplied by 105


123

Table 11 Imbalance–return relation during the financial crisis with and without size/liquidity effects

Conditional relation


~Ii;t 2521*** 2855*** 2639*** 2757***

~Ii;t�1 �234*** �617*** �370*** �665***

~Ii;t�2 �334*** �315*** �331*** �315***

~Ii;t�3 �214*** �196*** �209*** �195***

~Ii;t�4 �156*** �136*** �152*** �136***

~Ci;t 65*** 64***

~Ci;t � ~Ii;t �18 �7

~Ci;t�1 � ~Ii;t�1 �58*** �53***

~Cai;t

�58*** �58***

~Cai;t � ~Ii;t 5 �7

~Cai;t�1 � ~Ii;t�1 78*** 72***

~Si;t 49 43

~Si;t � ~Ii;t 279** 226

~Si;t�1 � ~Ii;t�1 212** 108

Adj. R2 (in %) 33.39 33.46 33.41 33.46

Unconditional relation


~Ii;t�1 288*** 20 151** �48

~Ii;t�2 �58 �44 �55 �44

~Ci;t�1 57*** 56***

~Ci;t�1 � ~Ii;t�1 �36*** �28**

~Cai;t�1

�52*** �52***

~Cai;t�1 � ~Ii;t�1 53*** 44***

~Si;t�1 45 41

~Si;t�1 � ~Ii;t�1 211** 162*

Adj. R2 (in %) 31.09 31.12 31.09 31.12

Fixed-effects panel regression, upper part Eqs. (5) (second column), (8) (third column), (10) (fourth

column), and Eqs. (8) and (10) combined (last column); lower part Eqs. (6) (second column), (9) (third

column), (11) (fourth column), and Eqs. (9) and (11) combined (last column). Dependent variable: daily

closing mid-quote return. Independent variables: concurrent and four lags (conditional) or two lags

(unconditional) of daily order imbalance, control and interaction variables consisting of the corresponding

order imbalance lag and market capitalization (incl. ‘‘abnormal values’’ as defined in Eq. (7)) or order

imbalance and percentage bid-ask spread, respectively. Stock-specific and time-specific effects are con-

trolled using the within transformation. t statistics and p values are based on robust standard errors

following Arellano (1987). Coefficients have been multiplied by 105


123

we create a sub-sample for the period from July 1, 2007 to Sept 30, 2009, and re-run

the regressions in Eqs. (5), (6), (8), (9), (10), (11), and the corresponding

combinations. Table 11 provides the results.

Conditional imbalance coefficients increase during the crisis period when

controlling for size and/or liquidity effects, cf. the top lines of Tables 8 and 11.

Unconditional imbalance coefficients remain largely unaffected, cf. the correspond-

ing lines in Tables 9 and 11. R2 increases during the crisis. The control variables’

market capitalization and abnormal market capitalization show higher effects during

the crisis period, with coefficients between twice and three times their values

computed from the entire sample.

For the conditional relation, concurrent interaction terms decrease in magnitude,

while lag 1 interaction terms increase in magnitude (sometimes subject to decreased

significance as mentioned above). For the unconditional relation, size interaction

terms decrease in magnitude, whereas liquidity interaction terms increase. To rule

out a possible increase in the number of large order imbalances as the cause for the

changes during the financial crisis, we compared the fractions of small, medium and

large order imbalances for the crisis sub-sample to those in the entire sample.

During the crisis, the fraction of small imbalances shows a small increase, while the

two categories of larger imbalances decrease slightly. Hence, the results in Table 11

are not driven by changes in the magnitude of order imbalances.

6 Summary

In this paper, we investigated effects of order flow imbalance on daily returns of

German stocks. In contrast to previous studies based on time series regressions, we

used fixed-effects panel regressions. For the conditional relation (including

concurrent order imbalance), our results confirm those of previous studies. For

the unconditional relation (which allows forecasting returns from past order

imbalance), our results are qualitatively in line with the literature, but the effects are

weaker. This may point to increased efficiency of stock markets in the first decade

of this century (this paper) compared to the 1990s (previous studies). We find

pronounced and stable size effects and somewhat weaker liquidity effects. The

general imbalance–return link in our sample is not driven by extreme order

imbalances. Concurrent imbalance effects turn out to be stronger during the

financial crisis. If information on canceled limit orders had been available for our

dataset, effects of order imbalance would have been even more pronounced. A

further limitation of our dataset is that it may not contain very large orders, which

may be filled through channels outside the stock exchange. This may explain why

we found decreasing effects for higher order imbalances, which is in contrast to

some previous studies.

An interesting direction for further research would be a more comprehensive

coverage and comparison of order imbalance effects across markets and observation

frequencies: the geographical focus of existing studies lies mainly on the U.S. and


123

some Asian countries, whereas there are hardly any results on other European

markets. This holds both for daily frequencies and for intra-day data.

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0

International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distri-

bution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and

the source, provide a link to the Creative Commons license, and indicate if changes were made.

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Order flow imbalance effects on the German stock market...ORIGINAL RESEARCH Order ﬂow imbalance...

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